27 citations · 81 across the 27 of their papers we have counts for
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Algebraic Addition Theorems
Mark B. Villarino
We present a self-contained development of the Weierstrass theory of those analytic functions (single-valued or multiform) which admit an algebraic addition theorem. We review the…
A Refinement of Ramanujan's Factorial Approximation
Michael D. Hirschhorn, Mark B. Villarino
We give an elementary proof for new strict upper and lower bounds for the correction term in Ramanujan's approximation for the factorial function
An integral inequality and the Ricatti-Bernoulli differential equation
Mark B. Villarino
We apply an integral inequality to obtain a rigorous \emph{a priori} estimate of the accuracy of the partial sum to the power series solution of the Ricatti-Bernoulli differential…
On the accuracy of the Chakrabarti-Hudson approximation to
Mark B. Villarino
We obtain rigorous upper and lower bounds for the error in the recent approximation for proposed by Chakrabarti and Hudson
The AGM Simple Pendulum
Mark B. Villarino
We present a self-contained development of Gauss' Arithmetic-Geometric Mean (AGM) and the work of A.E. Ingham who obtained rigorous error bounds for the AGM approximations to the p…